Consider a Diamond-Mortensen-Pissarides Model of two-sided search like the one we studied in class. We are going to consider some extensions and their implications in this problems set. Efficiency Wages Efficiency wages is a concept introduced by Janet Yellen. The concept is that the marginal product of labor is affected by the wage rate. Under this framework, the marginal product is a function of the real wage and labor hours so that mpn(n, w). Specifically, let it be this function, mpn(n, w) = n 1 (w w ) , 0 < < 1, 0 < < 1, w > 0 where w is the reservation real wage below which the worker chooses unemployment. The optimal decision making condition of firms continues to be that which we had in class, mpn(n, w) = + q FILLw q FILL where > 0, 0 < qFILL < 1 and is taken as given by the firm, and w > 0 is taken as given by the firm. The firm chooses how many vacancies to post and knows that vacancies vac transform into hours worked in the following way, n = q FILL vac. Assume that workers and firms separate from their jobs each period so that s = 1. Answer the following questions: 1. (3 points) TRUE, FALSE, or UNCERTAIN? The marginal product increases ceteris paribus as the level of hours worked increases. 2. (3 points) TRUE, FALSE, or UNCERTAIN? The marginal product increases ceteris paribus as the real wage increases. 3. (3 points) TRUE, FALSE, or UNCERTAIN? The marginal cost to vacancy posting ceteris paribus increases as the real wage increases. 4. (3 points) TRUE, FALSE, or UNCERTAIN? The marginal benefit to vacancy posting ceteris paribus increases as the real wage increases. 5. (2 points) Contrast your result in 4. to the answer you would have given if the same statement had been made about the standard model we discussed in class. 1 Long-Term Unemployment We will consider an extension to the DMP model we studied in class so that the probability of finding a job is affected by effort. Effort (e > 0) comes at a personal cost to households. Additionally, we will assume that the probability of finding a job affected by the length of an unemployment spell (T). Let the probability of finding a job P FIND be given by the following function of effort, length of unemployment, and some base probability 0 < p < 1 of finding a job which is taken as given, P FIND = e T p, 0 < < 1, T > 1, > 0 The marginal cost of searching for a job is now given by mul(1 + e ), where > 1. The marginal benefit continues to be [P FINDw + (1 P FIND)b]muc. Answer the following questions: 6. (4 points) TRUE, FALSE, or UNCERTAIN? For each additional unit of effort, the incremental increase in the probability of job finding is less than the incremental increase in personal cost. 7. (2 points) TRUE, FALSE, or UNCERTAIN? For each additional quarter spent in unemployment, the probability of finding a job increases. 8. (2 points) TRUE, FALSE, or UNCERTAIN? The marginal benefit to searching ceteris paribus increases as effort increases. 9. (2 points) TRUE, FALSE, or UNCERTAIN? The marginal benefit to searching ceteris paribus increases as the time spent in unemployment increases. 10. (2 points) TRUE, FALSE, or UNCERTAIN? The marginal cost to searching ceteris paribus increases as effort increases. 11. (2 points) TRUE, FALSE, or UNCERTAIN? The marginal cost to searching ceteris paribus increases as the time spent in unemployment increases.